Quantum game theory merges principles from quantum mechanics with game theory, exploring how quantum phenomena such as superposition and entanglement can influence strategic decision making. It offers a novel approach to analyzing and optimizing complex systems where traditional game theory may fall short. Congestion of passengers, if considered as a network, may fall into the categories of optimization cases of quantum games. This paper explores the application of quantum potential games to minimize congestion in common areas at airports. The players/passengers of the airport have identical interests and they share the same utility function. A metric is introduced that considers a passenger’s visit to a common area by setting their preferences, in order to avoid congestion. Passengers can decide whether to visit a specific common area or choose an alternative. This study demonstrates that the proposed game is a quantum potential game for tackling congestion, with identical interests, ensuring the existence of a Nash equilibrium. We consider passengers to be players that want to ensure their interests. Quantum entanglement is utilized to validate the concept, and the results highlight the effectiveness of this approach. The objective is to ensure that not all passengers select the same common place of the airport to reduce getting crowded; hence, the airborne disease infection probability increases due to overcrowding. Our findings provide a promising framework for optimizing passenger flow and reducing congestion in airport common areas through quantum game theory. We showed that the proposed system is stable by encapsulating the Lyapunov stability. We compared it to a simulated annealing approach to show the efficacy of the quantum game approach. We acknowledge that this framework can be utilized in other disciplines as well. For our future work, we will research different strategies than binary ones to investigate the efficacy of the approach.
Quantum game theory merges principles from quantum mechanics with game theory, exploring how quantum phenomena such as superposition and entanglement can influence strategic decision making. It offers a novel approach to analyzing and optimizing complex systems where traditional game theory may fall short. Congestion of passengers, if considered as a network, may fall into the categories of optimization cases of quantum games. This paper explores the application of quantum potential games to minimize congestion in common areas at airports. The players/passengers of the airport have identical interests and they share the same utility function. A metric is introduced that considers a passenger’s visit to a common area by setting their preferences, in order to avoid congestion. Passengers can decide whether to visit a specific common area or choose an alternative. This study demonstrates that the proposed game is a quantum potential game for tackling congestion, with identical interests, ensuring the existence of a Nash equilibrium. We consider passengers to be players that want to ensure their interests. Quantum entanglement is utilized to validate the concept, and the results highlight the effectiveness of this approach. The objective is to ensure that not all passengers select the same common place of the airport to reduce getting crowded; hence, the airborne disease infection probability increases due to overcrowding. Our findings provide a promising framework for optimizing passenger flow and reducing congestion in airport common areas through quantum game theory. We showed that the proposed system is stable by encapsulating the Lyapunov stability. We compared it to a simulated annealing approach to show the efficacy of the quantum game approach. We acknowledge that this framework can be utilized in other disciplines as well. For our future work, we will research different strategies than binary ones to investigate the efficacy of the approach.
Because of the sustained growth of information and mobile users transmitting a great amount of data packets, modern network performances are being seriously affected by congestion problems. In fact, congestion management is a challenging task that can be roughly summarized as a trade off between transmission latency and cost. In order to contribute to solve the congestion problem on communication networks, a novel framework based on a quantum game model is proposed, where network packets compete selfishly for their fastest route. Simulations show that final network routing and traveling times achieved with the quantum version outperform those obtained with a classical game model with the same options for packet transmission for both. Pareto optimality and Nash equilibrium are studied as well as the influence of simulated and real noise in the quantum protocol. This leads to the opportunity of developing full-stack protocols that may be capable of taking advantage of the quantum properties for optimizing communication systems. Due to its generality, this game approach can be applied both in classical complex networks and in future quantum networks in order to maximize the performance of the quantum internet.
Quantum games extend classical game theory into the quantum realm by incorporating quantum players and quantum strategies. Two-player quantum games have been widely studied and applied, among other areas, in optimization and decision-making. In this work, we introduce, formalize and analyze a novel class of three-player quantum games, referred to as Proxy Quantum Games (PQGs). In this setting, one player, the Controller, influences or governs the strategic operations executed by a second player, the Proxy, who, in turn, competes directly against a third player, the Opponent. The strategic influence is implemented via controlled unitary operations, whereby the Proxy’s available strategies are conditioned on the Controller’s quantum state. We further generalize the PQG framework by incorporating multiple Controllers acting on a common Proxy, thereby enabling the study of higher-order strategic interactions and multi-agent influence structures. The objective under consideration is the maximization of the Controller’s expected payoff, under various configurations of strategic control and entanglement. Comparative analyses are conducted between the PQG formulation and conventional multiplayer quantum games, highlighting key differences in strategic behavior and payoff distributions.
Quantum game theory (QGT) extends traditional game theory by using quantum mechanics to create new models for strategic decision-making. Traditional game theory provides effective tools for analyzing rational human interaction; yet it suffers from three main restrictions because it cannot properly handle uncertain situations, contradictory behavior, and complex relationships among agents. QGT addresses these challenges through its implementation of quantum phenomena, which enable strategic options that go beyond traditional mixed strategies. The extended system introduces fresh equilibrium solutions that allow easier resolution of standard problems. The chapter presents an organized structure to display QGT, which shows its value for strategic decision-making systems. The chapter shows fundamental concepts that link classical theories with quantum theories through its demonstration of how quantum strategies have developed from their original state to their present form, which expands traditional game models. The research investigates optimization methods, cybersecurity measures, economic systems, and artificial intelligence applications. The study identifies implementation obstacles and future research needs. The advanced QGT decision-making systems provide outstanding solutions that allow intelligent systems to interact with their environments and solve complex environmental problems.
Purpose The current paper is a brief review of the emerging field of quantum-like modelling in game theory. This paper aims to explore several quantum games, which are superior compared to their classical counterparts, which means either they give rise to superior Nash equilibria or they make the game fairer. For example, quantum Prisoners Dilemma generates Pareto superior outcomes as compared to defection outcome in the famous classical case. Again, a quantum-like version of cards game can make the game fairer, increasing the chance of winning of players who are disadvantaged in the classical case. This paper explores all the virtues of simple quantum games, also highlighting some findings of the authors as regards Prisoners Dilemma game. Design/methodology/approach As this is a general review paper, the authors have not demonstrated any specific mathematical method, rather explored the well-known quantum probability framework, used for designing quantum games. They have a short appendix which explores basic structure of Hilbert space representation of human decision-making. Findings Along with the review of the extant literature, the authors have also highlighted some new findings for quantum Prisoners Dilemma game. Specifically, they have shown in the earlier studies (which are referred to here) that a pure quantum entanglement set up is not needed for designing better games, even a weaker condition, which is classical entanglement is sufficient for producing Pareto improved outcomes. Research limitations/implications Theoretical research, with findings and implications for future game designs, it has been argued that it is not always needed to have true quantum entanglement for superior Nash Equilibria. Originality/value The main purpose here is to raise awareness mainly in the social science community about the possible applications of quantum-like game theory paradigm. The findings related to Prisoners Dilemma game are, however, original.
Abstract From a common point of view, quantum mechanics, psychology, and decision science disciplines try to predict how unruly systems (atomic particles, human behaviors, and decision makers’ choices) might behave in the future. Effective predicting outcome of a capacity allocation game under various allocation policies requires a profound understanding as how strategic reasoning of decision makers contributes to the financial gain of players. A quantum game framework is employed in the current study to investigate how performance of allocation policies is affected when buyers strategize over order quantities. The results show that the degree of being manipulative for allocation mechanisms is not identical and adopting adaptive quantum method is the most effective approach to secure the highest fill rate and profit when it is practiced under a reasonable range of entanglement levels.
Theory of quantum games is a new area of investigation that has gone through rapid development during the last few years. Initial motivation for playing games, in the quantum world, comes from the possibility of re-formulating quantum communication protocols, and algorithms, in terms of games between quantum and classical players. The possibility led to the view that quantum games have a potential to provide helpful insight into working of quantum algorithms, and even in finding new ones. This thesis analyzes and compares some interesting games when played classically and quantum mechanically. A large part of the thesis concerns investigations into a refinement notion of the Nash equilibrium concept. The refinement, called an evolutionarily stable strategy (ESS), was originally introduced in 1970s by mathematical biologists to model an evolving population using techniques borrowed from game theory. Analysis is developed around a situation when quantization changes ESSs without affecting corresponding Nash equilibria. Effects of quantization on solution-concepts other than Nash equilibrium are presented and discussed. For this purpose the notions of value of coalition, backwards-induction outcome, and subgame-perfect outcome are selected. Repeated games are known to have different information structure than one-shot games. Investigation is presented into a possible way where quantization changes the outcome of a repeated game. Lastly, two new suggestions are put forward to play quantum versions of classical matrix games. The first one uses the association of De Broglie's waves, with travelling material objects, as a resource for playing a quantum game. The second suggestion concerns an EPR type setting exploiting directly the correlations in Bell's inequalities to play a bi-matrix game.